# Reconciling Units in Jeans' Criterion Formula

In "Physics and Chemistry of the Solar System" Jeans' Criterion is given as:

$\frac{GmM}{R_c} = \frac{3mkT}{2}$

... To me this suggests that on the left we have Joules, and on the right we have kg$\cdot$joules.

I then went to some old lecture notes and found that the professor derived the Jean's Radius from:

$\frac{GM}{R_c} = \frac{3kT}{2}$

which also has (as far as I can tell) an issue with units. Can anyone help my understand what I'm missing with this equation?

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Your first and second equations are the same with a factor of $m$ removed from both sides. Are the $m$ on the left and right side different?
$$kT = \frac{GM\mu}{r}$$
where the left side is the energy per particle and on the right side $\mu$ is the mass per particle, and this is dimensionally consistent. This is basically the same as your second equation if the $\mu$ is added.